Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}5x-3y &= -7 \\ 5x+3y &= -4\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $3y = -5x-4$ Divide both sides by $3$ to isolate $y$ $y = {-\dfrac{5}{3}x - \dfrac{4}{3}}$ Substitute this expression for $y$ in the first equation. $5x-3({-\dfrac{5}{3}x - \dfrac{4}{3}}) = -7$ $5x + 5x + 4 = -7$ Simplify by combining terms, then solve for $x$ $10x + 4 = -7$ $10x = -11$ $x = -\dfrac{11}{10}$ Substitute $-\dfrac{11}{10}$ for $x$ back into the top equation. $5( -\dfrac{11}{10})-3y = -7$ $-\dfrac{11}{2}-3y = -7$ $-3y = -\dfrac{3}{2}$ $y = \dfrac{1}{2}$ The solution is $\enspace x = -\dfrac{11}{10}, \enspace y = \dfrac{1}{2}$.